# from the theory of proveit.logic.booleans.disjunction¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, Lambda, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Boolean, Equals, Forall, InSet, Or, TRUE
from proveit.numbers import Natural

In [2]:
# build up the expression from sub-expressions
expr = Lambda([m, n], Conditional(Forall(instance_param_or_params = [A_1_to_m, C_1_to_n], instance_expr = Equals(Or(A_1_to_m, TRUE, C_1_to_n), TRUE), domain = Boolean), And(InSet(m, Natural), InSet(n, Natural))))

expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(m, n\right) \mapsto \left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, C_{1}, C_{2}, \ldots, C_{n} \in \mathbb{B}}~\left(\left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor \top\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) = \top\right) \textrm{ if } m \in \mathbb{N} ,  n \in \mathbb{N}\right..

In [5]:
stored_expr.style_options()

no style options
In [6]:
# display the expression information
stored_expr.expr_info()

core typesub-expressionsexpression
0Lambdaparameters: 1
body: 2
1ExprTuple35, 38
2Conditionalvalue: 3
condition: 4
3Operationoperator: 5
operand: 8
4Operationoperator: 20
operands: 7
5Literal
6ExprTuple8
7ExprTuple9, 10
8Lambdaparameters: 11
body: 12
9Operationoperator: 40
operands: 13
10Operationoperator: 40
operands: 14
11ExprTuple29, 31
12Conditionalvalue: 15
condition: 16
13ExprTuple35, 17
14ExprTuple38, 17
15Operationoperator: 18
operands: 19
16Operationoperator: 20
operands: 21
17Literal
18Literal
19ExprTuple22, 30
20Literal
21ExprTuple23, 24
22Operationoperator: 25
operands: 26
23ExprRangelambda_map: 27
start_index: 37
end_index: 35
24ExprRangelambda_map: 28
start_index: 37
end_index: 38
25Literal
26ExprTuple29, 30, 31
27Lambdaparameter: 48
body: 32
28Lambdaparameter: 48
body: 33
29ExprRangelambda_map: 34
start_index: 37
end_index: 35
30Literal
31ExprRangelambda_map: 36
start_index: 37
end_index: 38
32Operationoperator: 40
operands: 39
33Operationoperator: 40
operands: 41
34Lambdaparameter: 48
body: 42
35Variable
36Lambdaparameter: 48
body: 43
37Literal
38Variable
39ExprTuple42, 44
40Literal
41ExprTuple43, 44
42IndexedVarvariable: 45
index: 48
43IndexedVarvariable: 46
index: 48
44Literal
45Variable
46Variable
47ExprTuple48
48Variable